EMPIRICAL LIKELIHOOD METHOD FOR MEAN INFERENCE WITH MISSING DATA

摘要

The inference about the population mean of missing response data with auxiliary covariates is considered. Under the missing at random assumption and a semiparametric model, an empirical likelihood based inferential procedure is developed. An empirical likelihood ratio test statistic is constructed based on the influence function theory. A nonparametric version of Wilks' theorem is shown to hold for the empirical likelihood ratio. Moreover, the proposed method is capable of combining information from auxiliary covariates and providing a more powerful empirical likelihood ratio test. The asymptotic power function is calculated under contiguous alternatives. Some simulation studies are carried out to examine the finite sample performances of the proposed method.